Adaptive filter model for motor vehicle sensor signals

ABSTRACT

A sensor system for combining first and second sensor signals, and generating a physical parameter values dependent on said sensor signals used in autocalibrating sensors improving the performance and quality of existing sensor signals and virtual sensors realizing new sensors by combining and integrating in adaptive filter models sensor signals representing same or different types of physical parameters.

FIELD OF THE INVENTION

The present invention relates generally to a system for integratingsensors of physical parameters, and more specifically to a system forsensor fusion in a wheeled vehicle.

BACKGROUND OF THE INVENTION

In the current development within vehicle technology there is anincreasing interest in enhancing the safety and the manoeuvrability ofvehicles by means of a number of support systems. Examples of well-knownsupport systems in wheeled vehicles are anti-lock brake systems (ABS),traction control systems and tire pressure estimation systems. This kindof systems are usually provided with more or less complex sensors suchas gyroscopes and wheel speed sensors to gather information aboutphysical parameters affecting the vehicle.

Along with the development of technology there is an increasing demandfor safety enhancing equipment in standard cars, something which is notalways compatible with an acceptable price level on this segment ofcars. There is therefore a need for developing cost efficient sensorequipment while improving the usability of the sensor signals.

An important parameter for automatic support systems, such as dynamicstability traction control (DSTC), is the course direction of thevehicle. The course is usually expressed in terms of the yaw angle,which is the direction of motion relating to a longitudinal axis of thevehicle, and the yaw rate, which is the angular velocity of the rotationof the vehicle around its centre of gravity in the horizontal plane.

In a simple approach, the yaw rate is independently calculated fromdifferent sensors in the vehicle, such as a gyro sensor, ABS sensors, anaccelerometer sensor or a steering wheel angle sensor, and thusresulting in different values of the yaw rate. These values have beencompared and voting has been used to decide which information to use.

Sensor signals generally comprise a parameter value and an offset fromthe true parameter value. The offsets are due to imperfect knowledge ofthe parameters and their dependencies, and the offsets vary in time dueto for example temperature changes and wear. An accurate estimation ofthe offsets is crucial to the ability of accurately estimating theparameter value itself. The traditional way to improve sensor signals isto use a low pass filter in order to get rid of high frequencyvariations, and sometimes an offset can be estimated using long termaveraging. Averaging has its shortcomings. For example in yaw rateestimation, a systematic circular driving will give the same effect asan offset. Furthermore, if two sensor signals measuring the samephysical parameter are averaged, an improved estimate of the parametermay be obtained but it does not help in estimating the offset.

The perhaps most well known support parameter for the driver of awheeled vehicle is the velocity. The vehicle velocity may be estimatedbased on the angular velocity of the driven wheel, however with aninaccuracy due to wheel slip, wheel skid or varying tire diameter. Thestandard approach to compute velocity is to use the wheel speed signalsfrom the wheel speed sensors and possibly averaging over left and rightwheels. To avoid errors due to wheel slip the non-driven wheels arepreferably used. This approach has however shortcomings during brakingwhen the wheels are locked and during wheel spin on 4 wheel-driven (WD)vehicles. For 4 WD vehicles an additional problem is that even duringnormal driving there will be a small positive velocity offset due to thewheel slip.

THE STATE OF THE ART

An example of the state of the art sensor utilisation is shown in U.S.Pat. No. 5,878,357 to Sivashankar et al. This piece of prior art isdirected to vehicle yaw rate estimation by a combination of a kinematicyaw rate estimation and a dynamic yaw rate estimation usingaccelerometers. A kinematic yaw rate estimate is weighted with a vehiclelateral acceleration at the centre of gravity, and steering angle andvehicle forward speed are incorporated into a Kalman filter forachieving a dynamic vehicle yaw rate estimate. This system usesrelatively low-cost sensor components but is sensitive to difficultdriving cases and errors in the wheel radii, for example due to varyingtire pressure. Another drawback is that it requires wiring through thewhole car in order to collect sensor signals from an accelerometer atthe front as well as the rear of the car.

Another example of prior art directed to yaw rate measuring is found inU.S. Pat. No. 5,274,576 to Williams. This prior art uses a solid staterate gyrometer, the accuracy of which is known to depend on the ambienttemperature. Measuring means provides a velocity signal, a steeringangle and a lateral acceleration signal, which are all used in acorrection means in order to remove bias errors from the output signalof the gyrometer. It is noted that this system is basically a low passfilter only compensating for long term bias errors.

The U.S. Pat. No. 5,860,480 to Jayaraman et al shows a method fordetermining pitch and ground speed of an earth moving machine, and isdirected to estimating certain operating parameters. This prior artseeks to overcome problems of noise and bias in sensor signals. Using asensor measurement model, a machine process model and Kalman filterupdate equations the pitch, the pitch rate and ground speed areestimated as a function of sensed pitch and ground speed signals.

The European Patent No. EP 0 595 681 A1 to Regie Nationale des UsinesRenault shows a method for determining the speed of a vehicle byprocessing sensed wheel angular velocity in a Kalman filter.

THE OBJECT OF THE INVENTION

The general problem to be solved by the present invention is to improvethe usability of signals from existing sensors measuring a firstphysical parameter.

Aspects of the problem are: to improve the accuracy of such sensorssignals;

-   to achieve a virtual sensor signal for a second physical parameter    dependent on said first physical parameter;-   to use and combine sensor information from different available    sources in order to achieve improved parameter estimates or virtual    sensor signals;-   to accurately estimate and eliminate offsets from parameter values    in the sensor signals.

A further and more specific aspect of the problem is to provide animproved computation of a course indication in the shape of yaw angleand yaw rate for a wheeled vehicle.

Yet another specific aspect of the problem is to provide an improvedestimation of the velocity of a wheeled vehicle.

A further aspect of the problem is to compute the actual fuel level andinstantaneous fuel consumption for any engine, where offset distortedmeasurements of the same quantities are available.

Yet another specific aspect is to compute the roll angle of a vehicle,in particular for motorcycles.

SUMMARY OF THE INVENTION

The object of the invention is achieved by processing a plurality ofsensor signals in an adaptive or recursive filter thereby producing anoptimized estimation of a first

The European Patent No. EP 0 595 681 A1 to Regie Nationale Des UsinesRenault shows a method for determining the speed of a vehicle byprocessing sensed wheel angular velocity in a Kalman Filter. The Kalmanfilter is based on a model that depends on an absolute reference, andmore specifically in the assumption that one of the sensor signals, i.e.the velocity signal, is free from errors, whereas an offset error ismodelled for the other signal, i.e. the acceleration signal. In case oferrors in the assumedly error free reference signals, this method willresult in erroneous parameter signal estimation. physical parameterdetected by said sensors. In accordance with the invention, aparticularly advantageous recursive filter is provided by a Kalmanfilter. In the invention, the Kalman filter is used as a framework forprocessing related sensor signals and estimating their respectiveoffsets. These related sensor signals do not necessarily have to measurethe same physical parameter, and in embodiments of the invention theyusually represent different parameters. Besides giving an accurateestimate of the offset, the Kalman filter also has the advantageouspossibility of attenuating noise.

The invention achieves an increase of performance in existing sensors byenhancing the sensor signal. Furthermore, new information is found bycombining and processing sensor signals and associate the result withother physical or operating parameters than those directly related withthe sensors.

According to an aspect of the invention, the accuracy of sensor signalsare highly improved by combining the signals of a plurality of existingor simple add-on sensors in the recursive filtering means.

According to another aspect of the invention, a virtual sensor signalfor a second physical parameter dependent on one or more first physicalparameters is generated by combining sensors of different type sensingdifferent first physical parameters by means of combined sensor signalsfrom real sensors. In other terms, all available information fromsensors in the vehicle is systematically fused in a recursive filter,preferably a Kalman filter.

When applying the sensor fusion in accordance with the invention incomputing a yaw rate value, at least two sensor signals are input into aKalman filter in order to minimize the error in an estimate signalrepresenting the yaw rate value. In a preferred embodiment, thesesensors signals are a yaw rate signal taken from a gyro, wheel speedsignals taken from an ABS equipment, possibly also a lateral yaw ratesignal computed from a lateral accelerometer and steering wheel anglesignals. An accurate yaw rate value can for example be applied inlateral slip computation, which is used in stability systems andfriction estimation. Furthermore, there are effects of the second order,for example an estimation of absolute tire radii and consequently alsoabsolute velocity. Moreover, the filtering process provides computationsof differences in tire radii as well as signals for diagnosis of faultsin the respective sensors. The diagnosis signals may be used to warn thedriver or be stored in a fault report to be used in connection withservice of the vehicle.

An accurate estimation of vehicle velocity is achieved in accordancewith an embodiment of the invention wherein wheel speed sensor signalsare combined with an accelerometer signal and processed in a filteringprocess in accordance with the above description. In accordance with theinvention, the velocity is accurately computed even during braking andwhen the wheels are locked. For a 4 WD vehicle or when non-driven wheelspeed signals are not available, the invention compensates for wheelslip and in addition to velocity also gives acceleration information.Other parameters that are derived in embodiments of the invention areslip-offset e.g. usable for tire pressure estimation in 4 WD vehicles,slip-slope e.g. usable for tire friction estimation in 2 WD and 4 WDvehicles, acceleration offset and the wheel velocity in the drivedirection. These embodiments as well as detection of aquaplaning areexamples of application of theory for the longitudinal stiffness oftires.

The slip of a vehicle wheel is a function of the momentum applied on awheel, wherein the slip-offset is a constant term of the function andthe slip-slope is the constant of proportionality between the appliedmomentum and the slip.

There are different further aspects that are relevant to different kindsof vehicles. Yaw rate and absolute velocity estimation is perhaps mostappropriate for cars and trucks. For motorcycles, the determination ofroll angle is important for an ABS and spin control, since less tireforcess can be utilised in cornering. Also, headlight control can beimplemented dependent on roll angle. Roll angle estimation isfurthermore crucial for roll-over detection, used in some airbag controlunits. Similarly to yaw rate estimation in cars, this can be done byusing wheel speed and a lateral-vertical accelerometer pair. Such a rollangle estimation carried out without using a roll gyro is an example ofa virtual sensor, where only indirect measurements are used to computethe physical quantity. It is here crucial to find and compensate for theaccelerometer offsets, which is conveniently achieved with the aid ofthe invention. As a further support, a roll gyro and longitudinalaccelerometer can be incorporated in the algorithm. Another example ofgreat practical importance is to detect aqua-planing quickly, for cars,trucks and motorcycles.

Other aspects and embodiments of the invention are disclosed in thedescription of detailed embodiments and the claims.

BRIEF DESCRIPTION OF THE DRAWINGS

The invention will now be further described by means of exemplifyingembodiments in conjunction with the accompanying drawings, in which:

FIG. 1A–1D show schematic block diagrams embodiments of the invention;

FIG. 2A shows schematically an embodiment of the invention applied inyaw rate computation;

FIG. 2B shows the invention applied in velocity computation;

FIG. 2C shows the invention applied in fuel consumption computation;

FIG. 2D shows the invention applied in slip slope computation;

FIG. 3A shows an embodiment of an autocalibrating sensor in accordancewith the invention;

FIG. 3B shows a schematic drawing which defines the geometric relationsof a four wheeled vehicle; and

FIG. 4 shows a plot diagram of an estimated offset in accordance withthe invention from an experimental test drive;

FIGS. 5A and 5B show coordinate systems and sensor configuration in amotorcycle;

FIG. 6 shows an embodiment of a virtual sensor for a roll angleindicator in a motorcycle;

FIG. 7 shows wheel geometry; and

FIG. 8 shows a schematic block diagram of a virtual sensor for an aquaplanning detector in accordance with an embodiment of the invention.

DETAILED DESCRIPTION OF EMBODIMENTS

The invention is based on the following general idea of sensor fusion,which is here described by way of example in terms of matrix algebra.This example relates to two sensors detecting the same physicalparameter, but in different embodiments of the invention signals fromsensors detecting different parameters may be integrated.

Two different sensors sensing the same varying physical parameter giveseparate measurements yi(t) of a the parameter x, where each measurementhas an offset bi with an offset scaling ci(t) according to a knownfunction of time. The measurements can be expressed algebraically as theequations:y1(t)=x(t)+c1(t)b1  (1)y2(t)=x(t)+c2(t)b2.  (2)These two equations have three unknowns and is therefore insoluble, andthe offsets cannot be directly eliminated.

When two measurements y1(1),y2(1) and y1(2),y2(2) are available, thereare two more equations and only one more unknown, i.e. four equationsand four unknowns. Thus, the offsets and the variable parameter valuesx(1),x(2) can be solved under the condition that there is no lineardependency in data In this example, the linear independency conditionis:c1(1)/c1(2)≠c2(1)/c2(2).  (3)

If, for example, c1 is constant and c2(t) is the velocity vx(t), linearindependency occurs when the velocity has changed between twomeasurements. This leads to observability and identifiability.Typically, measurements would be carried out by sensors delivering acontinuous or discrete sensor output signal which is sampled into adigital data processing system. The samples are collected in a per seknown manner with a predetermined sampling frequency, thus giving riseto a corresponding number of observations in the shape of equations toprocess.

In practice there is a measurement noise added to each of theobservations. In order to eliminate the noise, certain embodiments ofthe invention are devised to collect a number of observation sampleslarge enough to constitute an overdetermined equation system and tocompute the least square solution.

The invention also makes use of the a priori knowledge that theparameter variable x is a correlated sequence that cannot changearbitrarily fast between two samples. This property of the parametervariable x is used in a recursive filter, preferably a Kalman filter,into which the sampled observations input.

General Setting

The invention is generally implemented in a digital or analogue sensorcontrol system of a car. Such a system typically includes wired, opticalor wireless data communication links for communicating the output of asensor to a control unit. The control unit is provided with a dataprocessor, which in preferred embodiments is a digital processor havinga data storage memory and signal input and output ports. The digitalprocessor is programmed with a computer program product being providedwith means for directing the processor to perform the functions and thesteps of the inventive method. In an analogue implementation of theinventive concept, the control unit is provided with circuit elementsspecifically devised to perform the functions of the inventive method.

FIG. 1 shows a schematic diagram showing the functional blocks of theinvention. Sensors or sensor signal suppliers 102,104,106,108, capableof generating sensor signals S1,S2,S3,S4 dependent on or representing arespective physical parameter, are coupled to a sensor integration unit110. For example, in one embodiment the ABS is used as sensor signalsupplier 102, the sensor 104 is a gyro, the sensor 106 is one or moreaccelerometers and the engine is a sensor signal supplier 108. Thesensor integration unit comprises a recursive filter, preferably aKalman filter, devised to provide an estimate of a predeterminedphysical parameter, and outputs a physical parameter signal PSS1 to afirst sensor signal processing unit, more specifically a selfcalibrating sensor, here called a virtual sensor signal processing unit112. The virtual sensor signal processing unit 112 is devised to computeone or more virtual sensor signals VSS based on the physical parametersignal PSS1. The computed virtual sensor signal is for example the yawrate Ψ(dot), the velocity vx of the vehicle and the fuel consumption dVfuel/dt. The virtual sensor signal is then communicated to one or morecontrol units 118, for example devised for controlling an ABS, atraction control system, a dynamic stability traction control system(DSTC) or an adaptive cruise control system (ACC). A roll angle detectoris an example of both a virtual sensor when realised without a roll gyroand a self-calibrating sensor realised in conjunction with a roll gyro.The roll angle estimate can be used in roll-over detection in cars andfor improving ABS and anti-spin control and enabling headlight controlin motorcycles. With the help of these virtual signals, aqua-planing canbe detected with high reliability.

In the embodiment shown in FIG. 1, the sensor integration unit 110outputs a second physical parameter signal PSS2 to a second sensorsignal processing unit, which perhaps more properly constitutes avirtual sensor but in this figure is called an intelligent sensorprocessing unit 114, devised to compute a complementary, intelligentlycomputed sensor signal ISS used in a driver information processing unit120. Such intelligent sensor signals may for example represent frictionand tire conditions such as pressure or vibration. The sensorintegration unit 110 is also devised to deliver a third physical sensorsignal PSS3 communicated to third sensor signal processing unit in theshape of a diagnosis signal processing unit 116, which outputs adiagnose signal DSS to the driver information processing unit 120. Thedriver information processing unit in its turn outputs signals forexample indicating friction conditions, tire pressure or faults inpredetermined car components. Furthermore, a fourth physical parametersignal PSS4 may be delivered by the sensor integration unit to a fourthsensor signal processing unit, namely a vehicle control signalprocessing unit 117 devised to generate and deliver suitable vehiclecontrol signals VCS for example to vehicle operating apparatuses such asengine or brake control.

Self-Calibrating Sensor

FIG. 1B shows schematically the structure of a self-calibrating sensorin accordance with one embodiment of the invention, as explained inconnection with equations 1–3. Two sensor signals y1 and y2 representinga physical parameter are input into an adaptive filter 122 deviced toestimate in accordance with a predeterernined model and deliver as asoutput signal offsets b1(hat) and b2(hat). The sensor signals y1,y2 arealso input into an observability evaluation functionality together withpossible external info 128, the evaluation unit being deviced to outputan enable signal 125 to the adaptive filter 122 when the conditionsallow observability. The offset signal b1(hat) is joined with the sensorsignal y1 in a substraction stage 126 where the value of the offsetb1(hat) is substracted from the sensor signal value to produce a valueor a quantity of a parameter X.

FIG. 1C shows a general flow chart for the steps in a sensor fusionsystem, such as a self calibrating sensor in accordance with theinvention, comprising the following steps:

-   Initializing the system;-   Receiving as an input the next measurement or sample from the    sensors;-   Checking observability of parameter;-   If observability is OK then updating offset estimates;-   After uppdating of offset estimates or if observability is not OK    then compensate sensor signals with the offset output from the    adaptive filter.    Virtual Sensor

FIG. 1D shows schematically an example of a virtual sensor comprising anadaptive filter 136 based on a predetermined model integrating modelparameters values representing first and second different physical oroperating parameters. First and second sensor signals y1 and y2representing said first and second different parameters are input intothe filter 136 and into an observability evaluation unit 138. Theobservability evaluation unit 138 checks whether observability for thephysical parameters is fulfilled and if so outputs an enable signal 139to the adaptive filter 136. In enabled condition, the adaptive filter136 calculates and outputs an estimate of a physical quantity or valueX(hat) together with an estimate of offset values b1(hat) and b2(hat).The physical quantity X(hat) is the value of a physical model X as afunction f(y1,y2) dependent on the sensor signals y1 and y2.

Yaw Rate Computation

One embodiment of the invention is directed to achieve an adaptive highprecision yaw rate sensor by combining sensor signals from a gyro andfrom wheel angular velocity sensors of an ABS and by computing anaccurate yaw rate by means of an adaptive filter. Specific embodimentsmay comprise further sensor signals, for example the signals from alateral accelerometer, in order to further enhance the performance ofthe sensor. FIG. 2 shows schematically a yaw rate signal {dot over (ψ)}gyro 202 from a gyro and wheel angular speed signals 204 from an ABSbeing input in a filter 206 in accordance with the invention. The filter206 outputs a computed yaw angle ψ, yaw rate {dot over (ψ)} 208 as wellas yaw rate offset values.

FIG. 3A shows shematically a more detailed autocalibrating sensor fordetermining yaw rate, wherein a yaw rate signal {dot over (ψ)} from agyro and angular velocity signals ωi for the wheels are is input into anadaptive filter 301 as well as into an observability evaluation unit302. The evaluation unit 302 generates and inputs into the adaptivefilter an enable signal 304 when the sensed parameters are observable.The adaptive filter 301 generates as an output a yaw rate offset valueδgyro representing the offset of the yaw rate signal from the gyro. Theyaw rate {dot over (ψ)}0 and the offset value δgyro are joined in asummation unit 303 producing a {dot over (ψ)}-improved as an output.

FIG. 3B shows a simple drawing of a four wheeled vehicle, which drawingdefines the geometric relations for the wheel velocities duringcornering used to compute yaw rate from wheel speed signals. Morespecifically, the relations are used to compute the curve radius, whereR is defined as the distance to the centre of the rear wheel axle from apredetermined point O, L is the lateral distance between the wheels onone axle and B is the longitudinal distance between front and rear wheelaxle. The wheels are in this example denoted as rl for rear left, rr forrear right, fl for front left and fr for front right. A coordinatesystem indicating the x,y, and z-directions is also drawn in FIG. 3B.For the sake of clarity of the drawing, the coordinate system is drawnin front of the vehicle, but is in reality typically positioned in thecentre of gravity of the vehicle.

For the sake of simplicity of the explanation of the invention, thisexemplifying embodiment is based on relations assuming there is nolateral movement. In the relations:

$\begin{matrix}{{\overset{.}{\psi} = {\frac{v_{x}}{R} = {v_{x}R^{- 1}}}}{a_{y} = {\frac{v_{x}^{2}}{R} = {{v_{x}^{2}R^{- 1}} = {v_{x}\overset{.}{\psi}}}}}} & {(4),(5)}\end{matrix}$

-   {dot over (ψ)} is the yaw rate from a gyro;-   vx is the velocity of the vehicle in the x-direction;-   ay is the acceleration in the y-direction. The curve radius is    computed according to the following relation, where R is defined as    the distance to the center of the rear wheel axle,

$\begin{matrix}{\frac{v_{rr}}{v_{rl}} = {\frac{R_{rr}}{R_{rl}} = \frac{R + {L/2}}{R - {L/2}}}} & (6)\end{matrix}$

The angular wheel velocities ω for each of the respective wheels arereceived from an ABS and the inverse R⁻¹ of R is solved in order toavoid numerical problems in certain driving cases, e.g. driving straightahead. This results in

$\begin{matrix}{R^{- 1} = {{\frac{2}{L}\frac{\frac{v_{rl}}{v_{rr}} - 1}{\frac{v_{rl}}{v_{rr}} + 1}} = {\frac{2}{L}\frac{{\frac{\omega_{rl}}{\omega_{rr}}\frac{r_{rl}}{r_{rr}}} - 1}{{\frac{\omega_{rl}}{\omega_{rr}}\frac{r_{rl}}{r_{rr}}} + 1}}}} & (7)\end{matrix}$where the wheel radius is denoted r.

The wheel radii ratio is subject to an offset:

$\begin{matrix}{\frac{r_{rl}}{r_{rr}} \equiv {1 + \delta_{ABS}}} & (8)\end{matrix}$

The influence of the offset on the denominator is negligible, soaccording to embodiments of the invention the following expression isused for inverse curve radius:

$\begin{matrix}\begin{matrix}{R^{- 1} = {\frac{1}{L}\frac{2}{\frac{\omega_{rl}}{\omega_{rr}} + 1}\left( {{\frac{\omega_{rl}}{\omega_{rr}}\left( {1 + \delta_{ABS}} \right)} - 1} \right)}} \\{= {R_{m}^{- 1} + {\frac{1}{L}\frac{2}{\frac{\omega_{rl}}{\omega_{rr}} + 1}\frac{\omega_{rl}}{\omega_{rr}}\delta_{ABS}}}}\end{matrix} & (9)\end{matrix}$wherein the computable quantity

$\begin{matrix}{R_{m}^{- 1} = {\frac{1}{L}\frac{2}{\frac{\omega_{rl}}{\omega_{rr}} + 1}\left( {\frac{\omega_{rl}}{\omega_{rr}} - 1} \right)}} & (10)\end{matrix}$is used for the inverse curve radius.

Finally, the velocity at the center of the rear wheel axle is

$\begin{matrix}{v_{x} = {\frac{\omega_{rl} + \omega_{rr}}{2}r}} & (11)\end{matrix}$where r denotes the nominal wheel radius.

In a practical implementation of this embodiment, the sensormeasurements are:

-   y₁(t) from a yaw rate sensor, i.e. gyro signal;-   y₂(t)=v_(x)R_(m) ⁻¹, from ABS sensors, R_(m) ⁻¹ is computed as    above; and possibly-   y₃(t) from a lateral acceleration sensor.    It should be noted that when a lateral accelerometer is used, this    is preferrably supported by a vertical accelerometer to compensate    for non-horizontal movements of the vehicle.

All these sensor measurements are subject to an offset and measurementnoise given by the relations:

$\begin{matrix}{{{y_{1}(t)} = {{\overset{.}{\psi}(t)} + \delta_{YR} + {e_{1}(t)}}}\begin{matrix}{{y_{2}(t)} = {{v_{x}R_{m}^{- 1}} + {e_{2}(t)}}} \\{= {{\overset{.}{\psi}(t)} + {v_{x}\frac{1}{L}\frac{2}{\frac{\omega_{rl}}{\omega_{rr}} + 1}\frac{\omega_{rl}}{\omega_{rr}}\delta_{ABS}} + {e_{2}(t)}}}\end{matrix}{{y_{3}(t)} = {{v_{x}{\overset{.}{\psi}(t)}} + \delta_{ACC} + {e_{3}(t)}}}} & (12)\end{matrix}$where δABS is an offset that depends on relative tire radius betweenleft and right wheels.

As has been described above, the measurement signals are treated in afilter. A general filter description is given in the following section.In one embodiment, the offset is estimated by means of the least squaresmethod. So, eliminating the yaw rate from the first two measurementsyields a linear regression in the two offsets:y( t)=φ^(T)(t) δ+ē( t)  (13)where:

$\begin{matrix}{{{\overset{\_}{y}(t)} = {{y_{1}(t)} - {y_{2}(t)}}}{{\varphi(t)} = \left( {1,{v_{x}\frac{1}{L}\frac{2}{\frac{\omega_{rl}}{\omega_{rr}} + 1}\frac{\omega_{rl}}{\omega_{rr}}}} \right)^{T}}{\overset{\_}{\delta} = \left( {\delta_{YR},\delta_{ABS}} \right)^{T}}{{\overset{\_}{e}(t)} = {{e_{1}(t)} - {e_{2}(t)}}}} & (14)\end{matrix}$Using also an accelerometer, the regression quantities are

$\begin{matrix}{{{\overset{\_}{y}(t)} = {{y_{1}(t)} - \frac{y_{3}(t)}{v_{x}}}}{{\varphi(t)} = \left( {1,\frac{1}{v_{x}}} \right)^{T}}{\overset{\_}{\delta} = \left( {\delta_{YR},\delta_{ACC}} \right)^{T}}{{\overset{\_}{e}(t)} = {{e_{1}(t)} - \frac{e_{2}(t)}{v_{x}}}}} & (15)\end{matrix}$

The least squares estimate is computed by

$\begin{matrix}{\overset{\Cap}{\delta} = {\left( {\frac{1}{N}{\sum\limits_{i = 1}^{N}\;{{\varphi(t)}{\varphi^{T}(t)}}}} \right)^{- 1}\frac{1}{N}{\sum\limits_{i = 1}^{N}\;{{\varphi(t)}{y(t)}}}}} & (16)\end{matrix}$

The important question of identifiability, that is, under whatconditions are the offsets possible to estimate, is answered by studyingthe rank of the matrix to be inverted in the LS solution. For theaccelerometer sensor, the matrix is given by:

$\begin{matrix}{{\frac{1}{N}{\sum\limits_{i = 1}^{N}\;{{\varphi(t)}{\varphi^{T}(t)}}}} = \begin{pmatrix}1 & {\frac{1}{N}{\sum\limits_{i = 1}^{N}\;\frac{1}{v_{x}(t)}}} \\{\frac{1}{N}{\sum\limits_{i = 1}^{N}\;\frac{1}{v_{x}(t)}}} & {\frac{1}{N}{\sum\limits_{i = 1}^{N}\;\frac{1}{{v_{x}(t)}^{2}}}}\end{pmatrix}} & (17)\end{matrix}$In short, this matrix has full rank if and only if the velocity changesduring the time horizon. Furthermore, the more variation, the betterestimate. Similarly, the offsets are identifiable from yaw rate and ABSsensors if the velocity or the curve radius changes anytime. Inaccordance with the invention, the offsets are estimated adaptively byrecursive least squares (RLS) algorithm, least mean square (LMS) or aKalman filter.

In real time implementations of the invention, the Kalman filter ispreferred and improves the performance over RLS in the following way:

-   -   Firstly, a model for the variation of the true yaw rate can be        incorporated in the Kalman filter. For instance, the yaw rate        may be limited to 5 Hz maximum frequency variation.    -   Secondly, different time-variations of the sensor offsets can be        used. For instance, temperature can influence the gyro offset        variation, a cold start can make the filter forget more of the        gyro offset than the ABS offset.

The Kalman filter is completely specified by a state space equation ofthe formx(t+1)=Ax(t)+Bv(t)y(t)=Cx(t)+e(t)  (18)where the covariance matrices of v(t) and e(t) are denoted Q and R,respectively. The unknown quantities in the state vector x(t) areestimated by a recursion{circumflex over (x)}( t+1)=A{circumflex over (x)}(t)+K(t;A,B,C,Q,R)(y(t)−C x (t))  (19)where the filter gain K(t;A,B,C,Q,R) is given by the Kalman filterequations. Thus, the problem when designing an implementation is tosetup the state space model.

An exemplifying embodiment uses the state vector:

$\begin{matrix}{{x(t)} = \begin{pmatrix}{\overset{.}{\psi}(t)} \\{\overset{¨}{\psi}(t)} \\\delta_{YR} \\\delta_{ABS}\end{pmatrix}} & (20)\end{matrix}$and a continuous time state space model is:

$\begin{matrix}{{\overset{.}{x}(t)} = {{\begin{pmatrix}0 & 1 & 0 & 0 \\0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 \\0 & 0 & 0 & 0\end{pmatrix}{x(t)}} + {\begin{pmatrix}0 \\1 \\0 \\0\end{pmatrix}{v(t)}}}} & \left( {21a} \right) \\{{y(t)} = {{\begin{pmatrix}1 & 0 & 1 & 0 \\1 & 0 & 0 & {v_{x}\frac{1}{L}\frac{2}{\frac{\omega_{rl}}{\omega_{rr}} + 1}\frac{\omega_{rl}}{\omega_{rr}}}\end{pmatrix}{x(t)}} + {e(t)}}} & \left( {21b} \right)\end{matrix}$It is here assumed that there is an unknown input v(t) that affects theyaw acceleration, which is a common model for motion models, basicallymotivated by Newton's law F=ma.

A discrete time state space model:

$\begin{matrix}\begin{matrix}{{x\left( {t + 1} \right)} = {{\begin{pmatrix}1 & T_{s} & 0 & 0 \\0 & 1 & 0 & 0 \\0 & 0 & 1 & 0 \\0 & 0 & 0 & 1\end{pmatrix}{x(t)}} + {\begin{pmatrix}{T_{s}^{2}/2} \\T_{s} \\0 \\0\end{pmatrix}{v(t)}}}} \\{{y(t)} = {{\begin{pmatrix}1 & 0 & 1 & 0 \\1 & 0 & 0 & {v_{x}\frac{1}{L}\frac{2}{\frac{\omega_{rl}}{\omega_{rr}} + 1}\frac{\omega_{rl}}{\omega_{rr}}}\end{pmatrix}{x(t)}} + {e(t)}}}\end{matrix} & (22)\end{matrix}$is derived and is used by the Kalman filter.

Embodiments of the invention integrating information from wheel speedsignals and gyro are thus capable to give accurate yaw angle and yawrate measurements where the gyro offset and relative tire radiidifferences are estimated and compensated for. As an alternative, orfurther support, to ABS, one or several lateral accelerometers can beused to support the yaw rate sensor with a further yaw rate dependentsensor signal.

Simulations and experiments show that the accuracy in yaw rate, notregarding the offsets, is better than using any of the sensor typesseparately. FIG. 4 shows a plotted diagram 401 of a Kalman filterestimated gyro offset 403 compared with a very exact offline adjustedoffset 402, the diagram having the time in seconds on the x-axis andgyro offset in rad/s on the y-axis. The diagram of FIG. 4 is aregistration from an experimental test drive and shows that the Kalmanfilter estimation after a short transitional period converges with theoffline adjusted offset within a margin of a few percentages of offsetscale units.

A further advantage with the inventive concept is that the relativedifference in wheel radii on non-driven right and left wheels can bevery accurately estimated, which is advantageously used for tirepressure indication. In different embodiments the Kalman filter is usedas a combined parameter estimator for the offset as well as a filter foryaw rate. In an alternative embodiment, an adaptive filter is used toestimate the offset parameters. A further effect of the invention isthat it gives support for diagnosis of faults in gyro and accelerometer.

In a stepwise description of the embodiment for yaw rate estimation, theinventive method comprises the following steps:

-   (1) Collecting measurements from    -   (a) a yaw rate gyro    -   (b) ABS Sensors    -   (c) possibly a lateral accelerometer    -   (d) possibly wheel steering angle sensor-   (2) Preprocessing and filtering of raw sensordata    -   1 Scaling of sensor inputs to physical constants        yawrate=nom.scale_factor_gyro*rawinputgyro−nom.offset_gyro.    -   2 Low-pass filtering of yaw rate to reduce quantization and        noise error effects for instance averaging over a few samples.    -   3 Rotational synchronization of cog stamps to avoid cog        deformity error effects i.e. calculate wheel angular velocity by        using a full revolution of the wheel.    -   4 Similar treatment of sensors (c) and (d) to reduce known error        effects for instance low-pass filtering.    -   5 Performing simple diagnosis on sensors to take care of sensor        built-in diagnosis functions for instance sensors using a zero        level voltage to indicate internal failure.-   (3) Calculating filter inputs and parameters in error model    -   1 Calculate the inverse curve radii estimate from front axle        wheelage    -   2 Calculate the inverse curve radii estimate from rear axle        wheelage (with indices changed to wfl and wfr)    -   3 Calculate the vehicle velocity estimate from ABS sensors    -   4 Calculate the yaw rate estimate from front and rear wheelage    -   5 Calculate the wheel radii offset error propagation function        for rear axle    -   6 Calculate the wheel radii offset error propagation function        for front axle-   (4) Examine data quality by given norms to produce statistical    matrices for Kalman Filtering, for instance:

    1 Low velocity increases noise and other errors in yaw     rate fromABS sensors estimated       if (velocity_estimate < LOW_LEVEL)        Increase values in Kalman measurement covariance matrix R     2Standstill car assures yaw rate to be exactly zero       if(velocity_estimate == ABSOLUTE_ZERO)         Decrease values in Kalmanmeasurement covariance matrix R

-   (5) Applying the Kalman Filter equations    -   1 Time update of Kalman Filter        xhat=F*xhat;        Phat=F*Phat*F′+G*Q*G′;    -   2 Measurement update of Kalman Filter        K=Phat*H′*inv(H*Phat*H′+R);        e=y−H*xhat;        xhat=xhat+K*e;        Phat=Phat−K*H*Phat′;        Phat=0.5*(Phat+Phat′);        Where xhat is the current state estimate and Phat is the current        Kalman error covariance matrix, y is current measurement, H is        measurement matrix, F is state space model update matrix and G        is noise update matrix.-   (6) Output of yaw rate and offset estimates    -   1 Provide a fast yaw rate which is the current measured low-pass        filtered yaw rate minus the estimated offset to be used by for        instance time-critical control systems.    -   2 Provide a filtered yaw rate which is the current yaw rate        state estimate of the Kalman Filter to be used by for instance        navigation systems.    -   3 Provide relative wheel radii between left and right wheels on        rear and front wheelage to be used for instance by tire pressure        estimation systems.    -   4 Provide the rate gyro offset estimate to be used in diagnosis        functions.        Velocity Computation

One embodiment of the invention is concerned with applying the inventionfor velocity computation, or more generally expressed longitudinalmotion computation based on standard sensors of a vehicle. In accordancewith the invention, a sensor signal from an accelerometer ax isintegrated with a wheel angular velocity signal ω for example from anABS in a sensor signal integration unit 218. The sensor signalintegration unit comprises as explained above, a filtering process, andoutputs a computed velocity signal vx 220 and a computed accelerationsignal ax 222. As described above, an accelerometer sensing accelerationin the horizontal plane is preferably combined with a verticalaccelerometer for compensation for vertical motion. Since thisembodiment uses an accelerometer as a complement to the wheel speedsignals, the velocity can be computed after locking the wheels whenbraking.

The basic equations upon which the computation is based are similar tothose described above in connection with the yaw rate computation.Therefore, only the sensor signals to be fused and their characteristicsare shown here. Wheel angular speed signals ω are received from an ABSand are transformed to a scaled velocities at selected positions in thecar. The first sensor signal from the ABS is described by:

$\begin{matrix}{{y_{1}(t)} = {{{v_{x}(t)}\frac{1 + {k^{- 1}{\mu(t)}} + \delta}{r}} + {e_{1}(t)}}} & (23)\end{matrix}$wherein y1 is the angular velocity of a driving wheel;

-   -   vx is the absolute velocity of the wheel;    -   r is the wheel radius;    -   k is the slip-slope;    -   δ is the slip offset; and    -   μ is the wheel momentum.

The offset

$\begin{matrix}\frac{1 + {k^{- 1}{\mu(t)}} + \delta}{r} & (24)\end{matrix}$is here multiplicative, which means that the relations are non linearand the extended Kalman filter must be used. The sensor is accurate atmedium frequencies, at a time scale where the friction and tirecharacteristics k, δ are unchanged. The second sensor signal from anaccelerometer in longitudinal direction a_(x) is described by:y ₂(t)={dot over (v)} _(x)(t)+b ₂ +e ₂(t).  (25)Summing up to time t gives:

$\begin{matrix}{{{\overset{\_}{y}}_{2}(t)} = {{\sum\limits_{k = 0}^{t}\;{y_{2}(t)}} = {{v_{x}(t)} - {v_{x}(0)} + {b_{2}t} + {{\overset{\_}{e}}_{2}(t)}}}} & (26)\end{matrix}$

The offset scalings (l and t) are linearly independent if the tractionforce=μ(t) does not increase linearly in time, so the offsets b₂, k, δare observable. In this embodiment, offset and drift free velocity iscomputed from driven wheel speed and accelerometer with non-negligibleoffset for instance to be used in 4WD vehicles when free-rolling wheelsare not available. It also has a fast response to longitudinal velocitychanges during skid, i.e. spin or brake. Furthermore, the embodiment isadvantageously used for diagnosis of accelerometer. The system estimatesthe slip slope in a friction model which is also used to estimatetire-road friction.

In a stepwise description of the embodiment for velocity computation theinventive method comprises the following steps:

-   (1) Collection of measurements from    -   (a) a longitudinal accelerometer    -   (b) ABS Sensors    -   (c) possibly a yaw rate gyro-   (2) Preprocessing and filtering of raw sensordata    -   1 Scaling of sensor inputs to physical constants    -   2 Low-pass filtering of longitudinal acceleration measurement to        reduce quantization and noise error effects for instance        averaging over a few samples.    -   3 Rotational synchronization of cog stamps to avoid cog        deformity error effects i.e. calculate wheel angular velocity by        using a full revolution of the wheel.    -   4 Perform simple diagnosis on sensors to take care of sensor        built-in diagnosis functions for instance sensors using a zero        level voltage to indicate internal failure.-   (3) Calculation of filter inputs and parameters in error model    -   1 Calculate the vehicle velocity estimate from ABS sensors (Page        8—Eq 11)    -   2 Calculate the parameters in the error model (Page 12—Eq 23)    -   3 Calculate current matrices for the extended Kalman Filter (F,        G, H, Q)-   (4) Examine data quality by given norms to produce statistical    matrices for Kalman Filtering, for instance:

    1 Low velocity increases noise in velocity measurement     from ABSsensors       if (velocity_estimate < LOW_LEVEL)         Increase valuesin Kalman measurement covariance matrix R     2 Standstill car assuresvelocity to be exactly zero       if (velocity_estimate ==ABSOLUTE_ZERO)         Decrease values in Kalman measurement covariancematrix R

-   (5) Applying the Kalman Filter equations for the extended Kalman    Filter    -   1 Time update of Kalman Filter        xhat=F*xhat;        Phat=F*Phat*F′+G*Q*G′;    -   2 Measurement update of Kalman Filter        K=Phat*H′*inv(H*Phat*H′+R);        e=y−H*xhat;        xhat=xhat+K*e;        Phat=Phat−K*H*Phat′;        Phat=0.5*(Phat+Phat′);        Where xhat is the current state estimate and Phat is the current        Kalman error covariance matrix, y is current measurement, H is        measurement matrix, F is state space model update matrix and G        is noise update matrix.-   (6) Output of velocity and offset estimates    -   1 Provide a velocity estimate for control systems and MMI.    -   2 Provide wheel slips for 4WD vehicles    -   3 Provide the accelerometer offset estimate to be used in        diagnosis functions.        Fuel Level and Fuel Consumption Sensor

An embodiment of the invention is directed to computation of fuel leveland fuel consumption. This embodiment is schematically shown in FIG. 2Cand takes as an input a fuel volume signal 224 from the tank meter ofthe vehicle and a fuel injection signal 226 from the engine. The basicequations are again similar to those described above, however the sensorsignals are modelled according to the following equations.

Firstly, the tank level measurement is:y ₁(t)=V(t)+b ₁ +e ₁(t)  (27)This type of sensor usually suffers from medium-frequency disturbancesin the noise component e1(t), which is normally handled with a very slowlow-pass filter. On the other hand, low-frequency accuracy in the timeconstant of one re-fuelling is good. The offset depends inter alia onmanufacturing variations and temperature.

Secondly, a fuel injection signal tq or the like is transformed to amomentary fuel consumption signal described as:y ₂(t)={dot over (V)}(t)+b₂ +e ₂(t)  (28)This sensor is very good at high frequencies, basically since itmeasures derivatives.

Summing up to time t gives:

$\begin{matrix}{{{\overset{\_}{y}}_{2}(t)} = {{\sum\limits_{k = 0}^{t}\;{y_{2}(t)}} = {{V(t)} - {V(0)} + {b_{2}t} + {{\overset{\_}{e}}_{2}(t)}}}} & (29)\end{matrix}$The offset scalings 1 and t are linearly independent and therefore theoffsets are observable.

This in effect virtual sensor has the advantages of fast response afterre-fuelling, is an offset free monitor of momentary as well as averagevalues of fuel consumption, and is suitable to use for diagnosis offaults in fuel pipes and engine efficiency.

In a stepwise description of the embodiment for fuel consumption, theinventive method comprises the following steps:

-   (1) Collection of measurements from    -   (a) a tank level measurement device    -   (b) fuel injection signal-   (2) Preprocessing and filtering of raw sensordata    -   1 Scaling of sensor inputs to physical constants    -   2 Low-pass filtering of fuel injection measurement to reduce        quantization and noise error effects for instance averaging over        a few samples.    -   3 Perform simple diagnosis on sensors to take care of sensor        built-in diagnosis functions for instance sensors using a zero        level voltage to indicate internal failure.-   (3) Calculation of filter inputs and parameters in error model    -   1 Calculate the tank fuel level estimate from fuel level sensor    -   2 Calculate the fuel consumption from fuel injection signal-   (4) Examine data quality by given norms to produce statistical    matrices for Kalman Filtering, for instance:    -   1 High load on engine gives unreliable consumption results,        increase part of R-   (5) Applying the Kalman Filter equations    -   1 Time update of Kalman Filter        xhat=F*xhat;        Phat=F*Phat*F′+G*Q*G′;    -   2 Measurement update of Kalman Filter        K=Phat*H′*inv(H*Phat*H′+R);        e=y−H*xhat;        xhat=xhat+K*e;        Phat=Phat−K*H*Phat′;        Phat=0.5*(Phat+Phat′);        Where xhat is the current state estimate and Phat is the current        Kalman error covariance matrix, y is current measurement, H is        measurement matrix, F is state space model update matrix and G        is noise update matrix.-   (6) Output of fuel level fuel consumption and offset estimates    -   1 Provide fuel level for MMI systems.    -   2 Provide fuel consumption level for control systems and MMI        systems        Virtual Sensor for an Absolute Velocity Indicator

One embodiment of the invention is applied in velocity computation, ormore generally expressed longitudinal motion computation based onstandard sensors of a vehicle. In accordance with a variety of thisembodiment, a sensor signal from an accelerometer a_(x) is integratedwith a wheel angular velocity signal ω (for example from an ABS unit) ina sensor signal integration unit. The sensor signal integration unitcomprises, as explained above, a filtering process, and outputs acomputed velocity signal v_(x) and a computed acceleration signal a_(x).As described above, an accelerometer sensing acceleration in thehorizontal plane is preferably combined with a vertical accelerometerfor compensation for vertical motion. Since this embodiment uses anaccelerometer as a complement to the wheel speed signals, the velocitycan be computed also after locking the wheels when braking.

Wheel angular speed signals ω are received from an ABS and aretransformed to scaled velocities at selected positions in the car. Thefirst sensor signal from the ABS is described by

$\begin{matrix}{{y_{1}(t)} = {{{v_{x}(t)}\frac{1 + {k^{- 1}{\mu(t)}} + \delta}{r}} + {e_{1}(t)}}} & (30)\end{matrix}$where y₁ is the angular velocity of a driving wheel, v_(x) is theabsolute velocity of the wheel, r is the wheel radius, k is thelongitudinal stiffness, δ is the slip offset, μ is the normalizedtraction force, and e₁ is measurement noise.

The offset

$\frac{1 + {k^{- 1}{\mu(t)}} + \delta}{r}$(31 )is here multiplicative, which means that the relations arenon-linear and a non-linear observer or the extended Kalman filter mustbe used. The sensor is accurate at medium frequencies, at a time scalewhere the friction and tire characteristics, k and δ are unchanged.

The second sensor signal from an accelerometer in longitudinal directiona_(x) is described byy ₂(t)={dot over (v)} _(x)(t)+b ₂ +e ₂(t).

Summing up this equation to time t gives

$\begin{matrix}{{{\overset{\_}{y}}_{2}(t)} = {{\sum\limits_{k = 0}^{t}\;{y_{2}(t)}} = {{v_{x}(t)} - {v_{x}(0)} + {b_{2}t} + {{\overset{\_}{e}}_{2}(t)}}}} & (33)\end{matrix}$The offset scalings (l and t) are linearly independent if the normalizedtraction force μ(t) does not increase linearly in time, so the offsetsb₂, k, δ are observable.In this embodiment, offset and drift free velocity is computed fromdriven wheel speed and accelerometer with non-negligible offset forinstance to be used in 4WD vehicles when free-rolling wheels are notavailable. It also has a fast response to longitudinal velocity changesduring skid, i.e. spin or brake. Furthermore, the embodiment isadvantageously used for diagnosis of the accelerometer. The systemestimates the slip slope in a friction model which is also used toestimate tire-road friction.

In a stepwise description of the embodiment for velocity computation,the inventive method comprises the following steps:

-   (1) Collection of measurements from:    -   (a) a longitudinal accelerometer    -   (b) ABS Sensors    -   (c) possibly a yaw rate gyro-   (2) Preprocessing and filtering of raw sensordata:    -   Scaling of sensor inputs to physical constants    -   Low-pass filtering of longitudinal acceleration measurement to        reduce quantization and noise error effects for instance        averaging over a few samples.    -   Rotational synchronization of cog stamps to avoid cog deformity        error effects, i.e., calculate wheel angular velocity by using a        full revolution of the wheel.    -   Perform simple diagnosis on sensors to take care of sensor        built-in diagnosis functions for instance sensors using a zero        level voltage to indicate internal failure.-   (3) Calculation of filter inputs and parameters in error model:    -   Calculate the vehicle velocity estimate from ABS sensors    -   Calculate the parameters in the error model    -   Calculate current matrices for the extended Kalman Filter (F, G,        H, Q)-   (4) Examine data quality by given norms to produce statistical    matrices for Kalman Filtering, for instance:-   Low velocity increases noise in velocity measurement from ABS    sensors    -   if (velocity_estimate<LOW_LEVEL)    -   Increase values in Kalman measurement covariance matrix R-   Standstill car assures velocity to be exactly zero    -   if (velocity_estimate==ABSOLUTE_ZERO)    -   Decrease values in Kalman measurement covariance matrix R-   (5) Applying the Kalman filter equations for the extended Kalman    filter:    -   (a) Time update        {circumflex over (x)} _(k) =F _(k) {circumflex over (x)} _(k−1)        P _(k) =F _(k) P _(k−1) F _(k) ^(T) +G _(k) Q _(k) G _(k)        ^(T)  (33)    -   (b) Measurement update        K=P _(k) H _(k) ^(T)(H _(k) P _(k) H _(k) ^(T) +R _(k))⁻¹        ε_(k) =y _(k) −H _(k) {circumflex over (x)} _(k)        {circumflex over (x)} _(k) ={circumflex over (x)} _(k) +Kε _(k)        P _(k) =P _(k) −KH _(k) P _(k) ^(T)  (34)        Where {circumflex over (x)}_(k) is the current state estimate,        P_(k) is the current state error covariance matrix, and y_(k) is        current measurement. The state space matrices F_(k), G_(k) and        H_(k) are obtained by linearizing the non-linear state space        model around the current state estimate {circumflex over        (x)}_(k). The results and uses of velocity and offset estimates        in accordance with this embodiment are for example to provide a        velocity estimate for control systems and MMI (man machine        interface), to provide wheel slip indications or estimates for        4WD vehicles, and to provide an accelerometer offset estimate to        be used in diagnosis functions.        Sensor for a Roll Angel Indicator

An embodiment of the invention being applicable for a virtual sensor aswell as for an autocalibrating sensor is directed to achieve a rollangle indicator. By way of example, the described embodiment uses alateral and a vertical accelerometer, a yaw rate gyro and a velocityestimate. The measurement from the lateral accelerometer is denoteda_(y) and from the vertical accelerometer a_(z). The required velocityis in this example provided by the ABS by rescaling the angular velocitywith the wheel radius.

A common problem with accelerometers is a temperature dependent sensoroffset. This invention provides an alternative to the costly solution ofcalibrating all sensors during production also entailing that anadditional temperature sensor is required on each motorcycle. Anembodiment of the invention is adapted to estimate and compensate forthe sensor offsets automatically during driving.

Accelerometers and gyros typically deliver a continuous time signal. Inorder to use this signal in a discrete time system this signal must besampled using a suitable sampling rate. Alias effects are avoided byusing an anti alias filter (LP-filter) before the sampling. Outliersdeteriorates the performance of the system and are removed before thesensor fusion stage. The sensor fusion is performed using an adaptivefilter, preferrably a Kalman filter.

Models describing the accelerometers are derived using mechanicalengineeringe. The general expressions for an ideal lateral and an idealvertical accelerometer moving in a field of gravity are:a _(By) ={dot over (v)}+u{dot over (ψ)}−w{dot over (φ)}+x{umlaut over(ψ)}−z{umlaut over (φ)}+x{dot over (φ)}{dot over (θ)}−y({dot over(φ)}²+{dot over (ψ)}²)+z{dot over (θ)}{dot over (ψ)}+g sin Φ cos Θa _(Bz) ={dot over (w)}+v{dot over (φ)}−u{dot over (θ)}+y{umlaut over(φ)}−x{umlaut over (θ)}+x{dot over (φ)}{dot over (ψ)}+y{dot over(θ)}{dot over (ψ)}−z({dot over (φ)}²+{dot over (θ)}²)+g cos Φ cosΘ  (35)with notation for a motorcycle in accordance with the illustration ofcoordinate systems in FIG. 5A, the sensor configuration in FIG. 5B andaccording to the following.

Symbol Meaning u Longitudinal velocity {dot over (u)} Longitudinalacceleration v Lateral velocity {dot over (v)} Lateral acceleration wVertical velocity {dot over (w)} Vertical acceleration Φ Roll angle {dotover (ψ)} Angular velocity around local axle {circumflex over (x)}{umlaut over (ψ)} Angular acceleration around local axle {circumflexover (x)} Θ Pitch angle {dot over (θ)} Angular velocity around localaxle ŷ {umlaut over (θ)} Angular acceleration around local axle ŷ {dotover (Ψ)} Angular velocity around local axle {circumflex over (z)}{umlaut over (Ψ)} Angular acceleration around local axle {circumflexover (z)} x Position of sensor in coordinate axle {circumflex over (x)}y Position of sensor in coordinate axle ŷ z Position of sensor incoordinate axle {circumflex over (z)} g Gravity (g ≈ 9.81 [m/s²])

For a motorcycle is the lateral velocity v and vertical velocity wapproximately zero during normal driving. The expressions are furthersimplified if the location of the accelerometers are chosen to x=0, y=0and z=z_(x).

The sensor models are simplified toa _(By) =u{dot over (ψ)}−z _(x) {umlaut over (φ)}+z _(x) {dot over(θ)}{dot over (ψ)}+g sin Φ cos Θa _(Bz) =−u{dot over (θ)}−z _(x)({dot over (φ)}²+{dot over (θ)}²)+g cosΦ cos Θ  (36)If Θ is assumed to be constant equal to zero are

$\left\{ \begin{matrix}{\overset{.}{\theta} = {\overset{.}{\psi}{\tan\Phi}}} \\{\overset{.}{\Phi} = \overset{.}{\varphi}}\end{matrix}\quad \right.$It is now obvious that the local roll rate {dot over (φ)} is equal tothe global roll rate {dot over (Φ)} and also that {dot over (θ)} can beeliminated from the accelerometer models.a _(By) =u{dot over (ψ)}−z _(x)({umlaut over (φ)}+{dot over (ψ)}² tanΦ)+g sin Φa _(Bz) =−u{dot over (ψ)} tan Φ−z _(x)({dot over (φ)}²+{dot over (ψ)}²tan² Φ)+g cos ΦThe first term in the expressions, u{dot over (ψ)} or u{dot over (ψ)}tan Φ, is important for modelling high velocity turns. The increasednormal force on the motorcycle from the ground is explained by thisterm. The second term depends on the location of the sensor in{circumflex over (z)}^and the third is the influence from gravity.Unfortunately there are two allowed solutions to these two expressions.In order to improve the system is one more interpretation of the lateralmeasurement required. This interpretation is made using necessaryconditions to achieve state of equilibrium in steady state turning.

Using Newtons equations is the following expression derived

${g\;\cos\mspace{11mu}\Theta\;\sin\mspace{11mu}\Phi_{G}} = {{{- \frac{u\;\overset{.}{\psi}}{{mz}_{\tau}}}\left( {\frac{I_{f}}{r_{f}} + \frac{I_{r}}{r_{r}}} \right)} - \;{u\;\overset{.}{\psi}} + {\alpha_{1}^{\prime}\overset{¨}{\varphi}} + {\alpha_{2}^{\prime}\;\overset{.}{\theta}\;\overset{.}{\psi}}}$Symbol Meaning m Total mass, driver + motorcycle + load I_(f) Moment ofinertia front wheel I_(r) Moment of inertia rear wheel r_(f) Wheelradius front wheel r_(r) Wheel radius rear wheel α₁^(′) Parameterdependent on MC geometry α₂^(′) Parameter dependent on MC geometry z_(τ)Distance ground to center of mass Θ Tilt Φ_(G) Roll angle to the CoMdriver + MC

Introduce the parameter

$K = {\frac{1}{m}\left( {\frac{I_{f}}{z_{f\;\tau}r_{f}} + \frac{I_{r}}{z_{r\;\tau}r_{r}}} \right)}$which describes the physical properties of the particular type ofmotorcycle. Assuming Φ_(G)=Φ results ing cos Θ sin Φ=−u{dot over (ψ)}K−u{dot over (ψ)}+α ₁′{umlaut over(φ)}+α₂′{dot over (θ)}{dot over (ψ)}

Assume constant pitch angle {dot over (Θ)}=0 and use {dot over (θ)}={dotover (ψ)} tan Φg cos Θ sin Φ=−u{dot over (ψ)}K−u{dot over (ψ)}+α ₁′{umlaut over(φ)}+α₂′{dot over (ψ)}² tan Φ

Inserting this expression in the earlier derived expression for thelateral accelerometer yieldsa _(By)=α₁{umlaut over (φ)}+α₂{dot over (ψ)}² tan Φ−u{dot over (ψ)}Kwhere the new variables α₁ and α₂ are constants describing the geometryof the motorcycle but are not equal to α₁′ and α₂′.

There are now one model for the vertical and two models for the lateralaccelerometer available.a _(By) =u{dot over (ψ)}−z _(x) {umlaut over (φ)}+z _(x){dot over (ψ)}²tan Φ+g sin Φa _(Bz) =−u{dot over (ψ)} tan Φ− z _(x)({dot over (φ)}²+{dot over (ψ)}²tan ² Φ)+g cos Φa _(By)=α₁{umlaut over (φ)}+α₂{dot over (ψ)}² tan Φ−u{dot over (ψ)}K

A rate gyro model follows from that the rate gyro is attached in thelongitudinal direction {circumflex over (x)}and measures ideally theroll angle derivative or gyro={dot over (φ)}. There are now one sensormodel for the ideal vertical acceleromter, two models for the ideallateral acceleromter and one model for the ideal rate gyro. An improvedmodel is achieved if the model is extended with additive sensor offsets:a _(By) =u{dot over (ψ)}−z _(x) {umlaut over (φ)}+z _(x){dot over (ψ)}²tan Φ+g sin Φ+δ_(y)a _(Bz) =−u{dot over (ψ)} tan Φ− z _(x)({dot over (φ)}²+{dot over (ψ)}²tan ² Φ)+g cos Φ+δ_(z)a _(By)=α₁{umlaut over (φ)}+α₂{dot over (ψ)}² tan Φ−u{dot over (ψ)}K+δ_(y)gyro={dot over (φ)}+δ_(gyro)where the notation is as presented earlier and

Notation Meaning δ_(y) Sensor offset lateral accelerometer δ_(z) Sensoroffset vertical accelerometer δ_(gyro) Sensor offset gyro

The adaptive filter is in this embodiment implemented by means of anextended Kalman filter. A continuous time state space model is derivedand is then transformed to a discrete time state space model using perse known theory from linear systems and sampled systems. The continuoustime state space model for the system is{dot over (x)}=Ax+Bwz=h(x)+vThe state vector x consists of seven elements x=(x₁ x₂ x₃ x₄ x₅ x₆x₇)^(T), wherein:x₁=φ=Rotation around {circumflex over (x)}x₂={dot over (φ)}=Angular velocity around {circumflex over (x)}x₃={umlaut over (φ)}=Angular acceleration around {circumflex over (x)}x₄={dot over (ψ)}=Angular velocity around {circumflex over (z)}x₅=δ_(y)=Accelerometer offset lateral accelerometerx₆=δ_(z)=Accelerometer offset vertical accelerometerx₇=δ_(gyro)=Gyro offset.

${\overset{.}{x}(t)} = {{\underset{A}{\underset{︸}{\begin{pmatrix}1 & 0 & 0 & 0 & 0 & 0 & 0 \\0 & 1 & 0 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 0 & 0 & 0\end{pmatrix}}}{x(t)}} + {\underset{B}{\underset{︸}{\begin{pmatrix}0 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 0 \\1 & 0 & 0 & 0 & 0 \\0 & 1 & 0 & 0 & 0 \\0 & 0 & 1 & 0 & 0 \\0 & 0 & 0 & 1 & 0 \\0 & 0 & 0 & 0 & 1\end{pmatrix}}}{w(t)}}}$${z(t)} = {\underset{h{({x{(t)}})}}{\underset{︸}{\begin{pmatrix}{{{u(t)}x_{4}} - {z_{s}x_{3}} + {z_{s}x_{4}^{2}\tan\; x_{1}} + {g\;\sin\; x_{1}} + x_{5}} \\{{{- {u(t)}}x_{4}\tan\; x_{1}} - {z_{s}\left( {x_{2}^{2} + {x_{4}^{2}\tan^{2}x_{1}}} \right)} + {g\;\cos\; x_{1}} + x_{6}} \\{{\alpha_{1}x_{3}} + {\alpha_{2}x_{4}^{2}\tan\; x_{1}} - {{u(t)}x_{4}K} + x_{5}} \\{x_{2} + x_{7}}\end{pmatrix}}} + {v(t)}}$

The discrete time Kalman filter is writtenx _(k+1) =Fx _(k) +Gw _(k)z _(k) =h(x _(k))+v _(k)Where T is the sampling time. Derivation of F and G from A and B isstraightforward according to the theory for sampled systems.

$x_{k + 1} = {{\underset{F}{\underset{︸}{\begin{pmatrix}1 & T & {T^{2}/2} & 0 & 0 & 0 & 0 \\0 & 1 & T & 0 & 0 & 0 & 0 \\0 & 0 & 1 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 1 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 1 & 0 & 0 \\0 & 0 & 0 & 0 & 0 & 1 & 0 \\0 & 0 & 0 & 0 & 0 & 0 & 1\end{pmatrix}}}x_{k}} + {\underset{G}{\underset{︸}{\begin{pmatrix}{T^{3}/6} & 0 & 0 & 0 & 0 \\{T^{2}/2} & 0 & 0 & 0 & 0 \\T & 0 & 0 & 0 & 0 \\0 & T & 0 & 0 & 0 \\0 & 0 & T & 0 & 0 \\0 & 0 & 0 & T & 0 \\0 & 0 & 0 & 0 & T\end{pmatrix}}}w_{k}}}$$z_{k} = {\underset{h{({x{(t)}})}}{\underset{︸}{\begin{pmatrix}{{u_{k}x_{4}} - {z_{s}x_{3}} + {z_{s}x_{4}^{2}\tan\; x_{1}} + {g\;\sin\; x_{1}} + x_{5}} \\{{{- u_{k}}x_{4}\tan\; x_{1}} - {z_{s}\left( {x_{2}^{2} + {x_{4}^{2}\tan^{2}x_{1}}} \right)} + {g\;\cos\; x_{1}} + x_{6}} \\{{\alpha_{1}x_{3}} + {\alpha_{2}x_{4}^{2}\tan\; x_{1}} - {u_{k}x_{4}K} + x_{5}} \\{x_{2} + x_{7}}\end{pmatrix}}} + v_{k}}$

Writing the discrete time signal model z=h(x), the extended Kalmanfilter is applied as follows.x _(k+1) =f(x _(k))+g(x _(k))w _(k),z _(k) =h(x _(k))+v _(k)

Here f, g and h are nonlinear functions of the states x_(k). Define thematrices F, G and H according to:

$F_{k} = {\left. \frac{\partial{f_{k}(x)}}{\partial x} \middle| {}_{x = {\hat{x}}_{k/k}}H_{k}^{\prime} \right. = \left. \frac{\partial{h_{k}(x)}}{\partial x} \right|_{x = {\hat{x}}_{{k/k} - 1}}}$G _(k) =g _(k)({circumflex over (x)} _(k/k))

The linearized signal model be written asx _(k+1) =F _(k) x _(k) +G _(k) w _(k) +u _(k)z _(k) =H _(k) ′x _(k) +v _(k) +y _(k)whereu _(k) =f _(k)({circumflex over (x)} _(k/k))−F _(k) {circumflex over(x)} _(k/k)y _(k) =h _(k)({circumflex over (x)} _(k/k−1))−H _(k) ′{circumflex over(x)} _(k/k−1)andE[w _(k) w _(l) ′]=Qδ _(k1)E[v _(k) v _(l) ′]=Rδ _(k1)

The extended Kalman filter equations are then{circumflex over (x)} _(k/k) ={circumflex over (x)} _(k/k−1) +L _(k) [z_(k) −h _(k)({circumflex over (x)}_(k/k−1))]{circumflex over (x)} _(k+1/k) =f _(k)({circumflex over (x)} _(k/k))L _(k)=Σ_(k/k−1) H _(k)Ω_(k) ⁻¹Ω_(k) =H _(k)′Σ_(k/k−1) H _(k) +R _(k)Σ_(k/k)=Σ_(k/k−1)−Σ_(k/k−1) H _(k) [H _(k)′Σ_(k/k−1) H _(k) +R _(k)]⁻¹ H_(k)′ Σ_(k/k−1)Σ_(k+1/k) =F _(k) Σ_(k/k) F _(k) ′+G _(k) Q _(k) G _(k)′Initialisation is provided by: Σ_(0/−1)=P₀,x_(0/−1)={circumflex over(x)}₀.

The necessary matrices for the roll angle estimation problem using twoaccelerometers the velocity of the motorcycle and an extended Kalmanfilter are:

${{F_{k} = \frac{\partial{f_{k}(x)}}{\partial x}}}_{x = {\hat{x}}_{k/k}} = {\begin{pmatrix}1 & T & {T^{2}/2} & 0 & 0 & 0 & 0 \\0 & 1 & T & 0 & 0 & 0 & 0 \\0 & 0 & 1 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 1 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 1 & 0 & 0 \\0 & 0 & 0 & 0 & 0 & 1 & 0 \\0 & 0 & 0 & 0 & 0 & 0 & 1\end{pmatrix} = F}$$G_{k} = {{g_{k}\left( {\hat{x}}_{k/k} \right)} = \begin{pmatrix}{T^{3}/6} & 0 & 0 & 0 & 0 \\{T^{2}/2} & 0 & 0 & 0 & 0 \\T & 0 & 0 & 0 & 0 \\0 & T & 0 & 0 & 0 \\0 & 0 & T & 0 & 0 \\0 & 0 & 0 & T & 0 \\0 & 0 & 0 & 0 & T\end{pmatrix}}$$H_{k}^{\prime} = {\frac{\partial{h_{k}(x)}}{\partial x}{_{x = {\hat{x}}_{k - 1}}{= \begin{pmatrix}{{z_{s}{x_{4}^{2}\left( {1 + {\tan^{2}x_{1}}} \right)}} + {g\;\cos\; x_{1}}} & 0 & {- z_{s}} & {u_{k} + {2z_{s}x_{4}\tan\; x_{1}}} & 1 & 0 & 0 \\{{{- u_{k}}{x_{4}\left( {1 + {\tan^{2}x_{1}}} \right)}} - {2z_{s}x_{4}^{2}\tan\;{x_{1}\left( {1 + {\tan^{2}x_{1}}} \right)}} - {\sin\; x_{1}}} & {{- 2}z_{s}x_{2}} & 0 & {{{- u}\;\tan\; x_{1}} - {2z_{s}x_{4}\tan^{2}x_{1}}} & 0 & 1 & 0 \\{\alpha_{2}{x_{4}^{2}\left( {1 + {\tan^{2}x_{1}}} \right)}} & 0 & \alpha_{1} & {{2\alpha_{2}x_{4}\tan\; x_{1}} - {uK}} & 1 & 0 & 0 \\0 & 1 & 0 & 0 & 0 & 0 & 1\end{pmatrix}}}}$

All that remains in order to run the algorithm is the initialization.{circumflex over (x)}₀ is chosen to suitable values and the matrix P₀reflects the uncertainty of {circumflex over (x)}₀. One choice is{circumflex over (x)}₀=(0 0 0 0 0 0 0)^(T)

$P_{0} = \begin{pmatrix}0.05 & 0 & 0 & 0 & 0 & 0 & 0 \\0 & 0.01 & 0 & 0 & 0 & 0 & 0 \\0 & 0 & 0.01 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 0.01 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 1 & 0 & 0 \\0 & 0 & 0 & 0 & 0 & 1 & 0 \\0 & 0 & 0 & 0 & 0 & 0 & 1\end{pmatrix}$

The described mathematical expressions are employed for example in avirtual sensor as shown in FIG. 6, taking as an input a selection of yawsignal from gyro, lateral acceleration signal ay, vertical accelerationsignal az and wheel angular velocity signal ωf. The sensor signals arepreferably preprocessed by being low pass filtered in stage 602, sampledin stage 604 low pass filtered in stage 606 and data reduced in stage608. The angular velocity signal is preferably also rescaled in stage610. The thus preprocessed sensor signals are the input into an adaptivefilter 612 based on a model in accordance with the previous description.The output of the filter are values or signals for a roll angle, sensoroffsets and yaw rate.

Virtual Sensor for Fuel Level and Fuel Consumption

One embodiment of the invention is directed to computation of fuel leveland fuel consumption. This embodiment takes as an input a fuel volumesignal from the tank meter of the vehicle, and a fuel injection signalfrom the engine. The basic equations are again similar to thosedescribed in earlier sections, however the sensor signals are modelledaccording to the following equations.

Firstly, the tank level measurement is:y ₁(t)=V(t)+b ₁ +e ₁(t)This type of sensor usually suffers from medium frequency disturbancesin the noise component e₁ which is normally handled with a very slowlow-pass filter. On the other hand, low-frequency accuracy in the timeconstant of one re-fuelling is good. The offset depends inter alia onmanufacturing variations and temperature.

Secondly, a fuel injection signal tq or the like is transformed to amomentary fuel consumption signal described asy ₂(t)={dot over (V)}(t)+b ₂ +e ₂(t)This sensor is very good at high frequencies, basically since itmeasures derivatives. Summing up y₂ to time t gives:

${{\overset{\_}{y}}_{2}(t)} = {{\sum\limits_{k = 0}^{t}\;{y_{2}(t)}} = {{V(t)} - {V(0)} + {b_{2}t} + {{\overset{\_}{e}}_{2}(t)}}}$The offset scalings 1 and t are linearly independent and therefore theoffsets are observable.

This in effect virtual sensor has the advantages of fast response afterre-fuelling, is an offset free monitor of momentary as well as averagevalues of fuel consumption, and is suitable to use for diagnosis offaults in fuel pipes and engine efficiency.

In a stepwise description of the embodiment for fuel consumption, theinventive method comprises the following steps:

-   1. Collection of measurements from:    -   (a) a tank level measurement device;    -   (b) a fuel injection signal-   2. Preprocessing and filtering of raw sensor data:    -   (a) Scaling of sensor inputs to physical constants    -   (b) Low-pass filtering of fuel injection measurement to reduce        quantization and noise error effects for instance averaging over        a few samples.    -   (c) Perform simple diagnosis on sensors to take care of sensor        built-in diagnosis functions for instance sensors using a zero        level voltage to indicate internal failure.-   3. Calculation of filter inputs and parameters in error model:    -   (a) Calculate the tank fuel level estimate from fuel level        sensor    -   (b) Calculate the fuel consumption from fuel injection signal-   4. Examine data quality by given norms to produce statistical    matrices for Kalman Filtering, for instance:    -   (a) High load on engine gives unreliable consumption results,        increase part of R-   5. Applying the Kalman Filter equations    -   (a) Time update of Kalman Filter        {circumflex over (x)}=F _(k) {circumflex over (x)} _(k−1)        P _(k) =F _(k) P _(k−1) F _(k) ^(T) +G _(k) Q _(k) G _(k) ^(T)    -   (b) Measurement update of Kalman Filter        K=P _(k) H _(k) ^(T)(H _(k) P _(k) H _(k) ^(T) +R _(k))⁻¹        ε_(k) =y _(k) −H _(k) {circumflex over (x)} _(k)        {circumflex over (x)} _(k) ={circumflex over (x)} _(k) +Kε _(k)        P _(k) =P _(k) −KH _(k) P _(k) ^(T)        where {circumflex over (x)}_(k) is the. The state space matrices        F_(k), G_(k) and H_(k) are obtained by linearizing the non        current state estimate, P_(k) is the current state error        covariance matrix, and y_(k) is the current measurement—linear        state space model around the current state estimate {circumflex        over (x)}_(k).-   6. Output of fuel level fuel consumption and offset estimates    -   (a) Provide fuel level for MMI systems.    -   (b) Provide fuel consumption level for control systems and MMI        systems        Virtual Sensor for Aqua Planning Detection

One embodiment of the invention is directed to automatic aqua planningdetection (APD) based on the following principles. The measured signalsand computed quantities that are utilized by the virtual sensor APD aresummarized shown in FIG. 7 and the following table.

Symbol Description ω_(d) Angular velocity, driven wheel [rad/s] ω_(n)Angular velocity, non-driven wheel [rad/s] r_(d) Wheel radius, drivenwheel [m] r_(n) Wheel radius, non-driven wheel [m] T_(e) Engine torque[Nm] i Gearing ratio from engine to driven wheels [−] N Normal force atdriven wheel [N] s Wheel slip [−] μ Normalized traction force [−]

FIG. 8 shows a schematic view of the functional components in a varietyof this embodiment, viz vehicle signals 802 are input into aprecomputation or preprocessing stage 804. The precomputed output is thefiltered in an adaptive filtering process stage 806 in accordance withthe inventive concept producing output parameter signals that aresubject to evaluation or used in a diagnosis in stage 808.

The virtual sensor APD detects aqua planning by monitoring thelongitudinal stiffness k, which during normal driving conditions can bemodeled as

${k = \frac{\mu}{s}},{where}$ $\mu = \frac{T_{e}i}{2\; r_{d}N}$is the normalized traction force and

$s = {\frac{{\omega_{d}r_{d}} - {\omega_{n}r_{n}}}{\omega_{n}r_{n}} = {\frac{\omega_{d}r_{d}}{\omega_{n}r_{n}} - 1}}$is the wheel slip. Here N is the tire normal force that depends on themass, the vehicle geometry and the vehicle state (such as the currentvelocity and acceleration/retardation). In case of aqua planning, thelack of friction between the tire and the road gives rise to anincreased wheel slip s if the traction force μ is maintained. Therefore,it is possible to detect aqua planning by monitoring sudden decreases inthe estimated slope parameter k. In practice it is necessary to takeinto account that the wheel radii r_(d) and r_(n) are unknown. Byintroducing δ as the relative difference in wheel radii, i.e.,

${\delta = \frac{r_{n} - r_{d}}{r_{n}}},$and approximating the wheel slip as

${\delta = \frac{r_{n} - r_{d}}{r_{n}}},$and approximating the wheel slip as

${s_{m} = {\frac{\omega_{d}}{\omega_{n}} - 1}},$obtains the model

${s_{m} \approx {s + \delta}} = {{\frac{1}{k}\mu} + {\delta.}}$The parameters in this model, 1/k and δ, are estimated from measuredslip s_(m) and traction force μ using an adaptive filter, such as arecursive least squares algorithm or a Kalman filter and the state spacemodelx _(1+l) =x ₁ +w ₁,s _(m,i) =H ₁ x ₁ +e ₁,where x₁=(1/k δ)^(T), H₁=(μ, 1)^(T), and w_(r) and e_(r) are process andmeasurement noise respectively.

The invention has been described by means of exemplifying embodimentsfor different applications and it should be appreciated that severaldesigns are possible within the inventive concept and as defined in theclaims.

1. A method of calculating a physical parameter value (X) of a wheeledvehicle indirectly using at least two directly measurable input signals,comprising the steps of: (a) receiving a first input sensor signal(y1(t)) that is dependent on a first physical input parameter affectinga condition of the wheeled vehicle; (b) receiving a second input sensorsignal (y2(t)) that is dependent on a second physical input parameteraffecting a condition of the wheeled vehicle, wherein the secondphysical input parameter can be any one of the same as physicalparameter value (X), the same as the first physical input parameter, anddifferent from the first physical input parameter; (c) recursivelyfiltering the first and second physical input parameters by means of anadaptive filter based on a predetermined model of the condition of thewheeled vehicle, wherein the input signals to said model include thefirst physical input parameter (y1(t)), the second physical inputparameter (y2(t)), a first offset scaling factor (c1(t)) for the firstsensor signal, and a second offset scaling factor (c2(t)) for the secondsensor signal, and wherein the model output signals include a firstoffset error signal (b1(t)) and a second offset error signal (b2(t)),and the physical parameter value (X); (d) estimating the values of saidfirst offset error (b1(t)) and the second offset error (b2(t)) by meansof said adaptive filter, wherein at least one offset error relates tothe wheel radius; and (e) calculating the physical parameter value (X)using the adaptive filter from the input sensor signals y1(t) and y2(t)such that offset errors in the calculation are compensated for by meansof the first and second offset error parameters (b1(t)) and (b2(t)) andthe offset scaling factors c1(t) and c2(t).
 2. The method of claim 1,wherein the model is based on relations between measured values (y(t))of said physical parameter (x(t)) and offsets (b1,b2) for said first andsecond sensor signals corresponding to the algebraic expressiony1(t)=x(t)+c1(t)b1y2(t)=x(t)+c2(t)b2, where y1(t) is a measurement of said physicalparameter x(t) detected by means of a first sensor and represented bysaid first sensor signal having said first offset error b1 and a firstoffset scaling c1(t) according to a predetermined function of time; andwhere y2(t) is a measurement of said physical parameter x(t) detected bymeans of a second sensor and represented by said second sensor signalhaving said second offset error b2 and a second offset scaling c2(t)according to a predetermined function of time.
 3. The method of claim 1,wherein the model is based on relations between measured values (yi(t))of said physical parameter (x(t)) and offsets (bi(t)) for a number i ofsensor signals corresponding to the algebraic expressionyi(t)=x(t)+ci(t)bi(t), where yi(t) is a measurement of said physicalparameter X(t) detected by means of a sensor number i and represented bya sensor signal having an offset error bi and an offset scaling ci(t)according to a predetermined function of time.
 4. The method of claim 1,further comprising the steps: evaluating the observability of saidphysical parameter; and updating offset measurements if a predeterminedobservability criterion met.
 5. The method of claim 4, furthercomprising the step of using external information in the observabilityevaluation.
 6. The method of claim 4, further comprising the steps of:initializing the sensor and filter system; receiving as an input thenext measurement or sample of said sensor signals; checking theobservability of said physical parameter; if observability is met, thenupdating offset estimates; after updating of offset estimates or ifobservability is not met, then compensate sensor signal with the offsetoutput from the adaptive filter.
 7. The method of claim 1, furthercomprising the steps of receiving a third sensor signal dependent on athird physical parameter affecting the condition of the wheeled vehicleand recursively filtering said third sensor signal together with saidfirst and second sensor signals by means of said adaptive filter, whichis based on a model that also is dependent on said third physicalparameter and on the offset error for said third sensor signal.
 8. Themethod of claim 1, wherein said filter is based on a model that also isdependent on measurement noise in the sensor signals respectively andfurther comprises the step of calculating and eliminating themeasurement noise of the calculated physical parameter value signal. 9.The method of claim 1, wherein said filter is based on a recursive leastmeans square algorithm (RLS).
 10. The method of claim 1, wherein saidfilter is based on a least means square algorithm (LMS).
 11. The methodof claim 1, wherein said filter is based on a Kalman filter.
 12. Themethod of claim 11, wherein said Kalman filter is specified by means ofa state space equation of the form:x(t+1)=Ax(t)+Bv(t)y(t)=Cx(t)+e(t) where the covariance matrices of v(t) and e(t) aredenoted Q and R, respectively, and wherein the unknown quantities in astate vector x(t) are estimated by a recursion:{circumflex over (x)}(t+1)=A{circumflex over(x)}(t)+K(t;A,B,C,Q,R)(v(i)−C{circumflex over (x)}(t)) where the filtergain K(t;A,B,C,Q,R) is given by predetermined Kalman filter equations.13. The method of claim 12, wherein said Kalman filter incorporates amodel for the variation of the true physical parameter value of thewheeled vehicle.
 14. The method of claim 1, further comprising the stepsof: examining the data quality according to predetermined rules;producing statistical matrices for Kalman filtering dependent on saidrules.
 15. The method of claim 14, wherein said rules are: if (velocityestimate <LOW_LEVEL) (then increase values in Kalman measurementcovariance matrix R and if (velocity estimate=ABSOLUTE_ZERO) (thendecrease values in Kalman measurement covariance matrix R.
 16. Themethod according to claim 1, further comprising applying Kalman filterequations by means of the steps of: time updating the Kalman filterxhat=F*xhat;Phat=F*Phat*F′+G*Q*G′; measurement updating the Kalman filterK=Phat*H′*inv(H*Phat*H′+R);e=y−H*xhat;xhat=xhat+K*e;Phat=Phat−K*H*Phat′;Phat=0.5*(Phat+Phat′); where xhat is the current state estimate and Phatis the current Kalman error covariance matrix, y is the currentmeasurement, H is measurement matrix, F is state space model updatematrix and G is noise update matrix.
 17. The method of claim 1, furthercomprising pre-processing raw sensor data by scaling sample sensorsignals to physical constants according to the model such that eachphysical constant is set equal to a nominal scale factor multiplied withthe raw sensor data value minus a nominal sensor offset.
 18. The methodof claim 17, further comprising pre-processing raw sensor data bylow-pass filtering sensor signal values in order to reduce quantisationerrors and noise errors.
 19. The method of claim 1, further comprisingpre-processing raw sensor data by rotationally synchronising clockstamps from cog-wheels by calculating wheel angular velocity to avoidcog deformity error effects.
 20. The method of claim 1, furthercomprising the step of providing an offset estimate to said sensorsignals for use in diagnosis functions.
 21. The method of claim 1,further being adapted for determining the yaw rate of said wheeledvehicle, wherein said first sensor signal is a yaw rate signal from ayaw rate gyro mounted in the wheeled vehicle; wherein said second sensorsignals are angular wheel velocity signals from angular wheel velocitysensors mounted in the wheeled vehicle for sensing the angular velocityof the wheels respectively; wherein said model is dependent on said yawrate signal, said angular wheel velocity signals, the offset error forthe yaw rate signal and the offset errors for the angular wheel velocitysignals; and wherein said delivered physical parameter value signal is acalculated yaw angle and a calculated yaw rate signal.
 22. The method ofclaim 21, further comprising the steps of receiving a third sensorsignal dependent on a third physical parameter affecting the conditionof the wheeled vehicle and recursively filtering said third sensorsignal together with said first and second sensor signals by means ofsaid adaptive filter, which is based on a model that also is dependenton said third physical parameter and on the offset error for said thirdsensor signal; wherein said third sensor signal is an accelerationsignal from an accelerometer mounted in the wheeled vehicle for sensinga lateral acceleration and wherein said adaptive filter is based on amodel that is also dependent on said lateral acceleration signal and onthe offset error for said acceleration signal.
 23. The method of claim21, further comprising the steps of calculating and eliminatingmeasurement noise from the calculated yaw rate signal.
 24. The method ofclaim 21, wherein said Kalman filter incorporates a model for thevariation of the true yaw rate of the wheeled vehicle.
 25. The method ofclaim 21, further comprising the steps of calculating offset errors forsaid angular wheel velocity signals and calculating the relativedifference in wheel radii between right and left wheels dependent onsaid offset errors for wheel velocity signals.
 26. The method of claim21, further comprising calculating filter input signals and parametersin an error model by the steps of: calculating an inverse curve radiusestimate from front axle wheels of the wheeled vehicle; calculating aninverse curve radius estimate from rear axle wheels of the wheeledvehicle; calculating vehicle velocity estimate from the angular wheelvelocity sensors; calculating yaw rate estimates from front and rearwheels; calculating an error propagation function for wheel radiusoffsets for a rear axle of the wheeled vehicle; calculating an errorpropagation function for wheel radius offsets for a front axle of thewheeled vehicle.
 27. The method of claim 21, further comprising the stepof providing a fast yaw rate which is the current measured low-passfiltered yaw rate minus the estimated offset for use in time criticalcontrol systems.
 28. The method of claim 21, further comprising the stepof providing a filtered yaw rate which is the current yaw rate stateestimate of the Kalman filter.
 29. The method of claim 21, furthercomprising the step of providing relative wheel radii between left andright wheels on rear and front wheelage to be used in a tire pressureestimation system.
 30. The method of claim 21, further comprising thestep of providing a yaw rate gyro offset estimate to be used in adiagnosis function.
 31. The method of claim 1, further adapted fordetermining longitudinal movement of said wheeled vehicle, wherein saidfirst sensor signal is an acceleration signal from an accelerometermounted in the wheeled vehicle; wherein said second sensor signals areangular wheel velocity signals from angular wheel velocity sensorsmounted in the wheeled vehicle for sensing the angular velocity of therespective wheels; wherein said model is dependent on said accelerationsignal, said angular wheeled velocity signals, the offset error for theacceleration signal and the offset errors for the angular wheel velocitysignals; and wherein said delivered physical parameter value signal is acalculated longitudinal velocity signal and a calculated longitudinalacceleration signal.
 32. The method of claim 31, wherein the adaptivefilter is an extended Kalman filter.
 33. The method of claim 31, furthercomprising the steps of: receiving a third sensor signal dependent on athird physical parameter affecting the condition of the wheeled vehicleand recursively filtering said third sensor signal together with saidfirst and second sensor signals by means of said adaptive filter, whichis based on a model that also is dependent on said third physicalparameter and on the offset error for said third sensor signal; whereinsaid third sensor signal is a yaw rate signal for the wheeled vehicleand wherein said adaptive filter is based on a model that is dependentalso on said yaw rate signal and on the offset error for said yaw ratesensor signal.
 34. The method of claim 31, further comprisingcalculation of filter input signals and parameters in an error model bythe steps of: calculating a vehicle velocity estimate from angularvehicle velocity sensors; calculating the parameters in the error model;calculating current matrices for an extended Kalman filter (F,G,H,Q).35. The method of claim 31, further comprising the step of providing avelocity estimate for a control system and an MMI (Man MachineInterface).
 36. The method of claim 31, further comprising the step ofproviding wheel slip values.
 37. The method of claim 31, furthercomprising the step of providing an accelerometer offset estimate foruse in a diagnosis function.
 38. The method of claim 1, further beingadapted for determining fuel level and fuel consumption of said wheeledvehicle: wherein said first sensor signal is a fuel volume signal from atank meter of the wheeled vehicle; wherein said second sensor signal isa fuel injection sensor signal from the engine of the wheeled vehicle;wherein said model is dependent on said fuel volume signal, said fuelinjection signal, the offset error for the fuel volume signal and theoffset error for the fuel offset signal; and wherein said deliveredphysical parameter value signal is a calculated fuel level and acalculated fuel consumption signal.
 39. The method of claim 38, furthercomprising calculation of filter input signals and parameters in anerror model by the steps of: calculating a fuel level estimate from thefuel level sensor signal; calculating the fuel consumption from the fuelinjection signal.
 40. The method of claim 38, further comprising thesteps of: examining the data quality according to the predeterminedrules; using statistical matrices for Kalman filtering dependent on saidrules.
 41. The method of claim 40, wherein said rules for examining thedata quality is: if high load on engine then increase part of values inthe Kalman measurement covariance matrix R.
 42. The method of claim 38,further comprising the step of providing the fuel level estimate for anMMI system (Man Machine Interface).
 43. The method of claim 38, furthercomprising the step of providing a fuel consumption estimate for acontrol system and an MMI system (Man Machine Interface).
 44. The methodof claim 1, wherein analytical redundancy is arranged for the adaptivefilter by generating a number of equations to process in said filter.45. An apparatus for calculating a physical parameter value (X) of awheeled vehicle indirectly using at least two directly measurable inputsignals, comprising: (a) a first input sensor signal (y1(t)) that isdependent on a first physical input parameter affecting a condition ofthe wheeled vehicle; (b) a second input sensor signal (y2(t)) that isdependent on a second physical input parameter affecting a condition ofthe wheeled vehicle, wherein the second physical input parameter can beany one of the same as physical parameter value (X), the same as thefirst physical input parameter, and different from the first physicalinput parameter; (c) means for recursively filtering the first andsecond physical input parameters by means of an adaptive filter based ona predetermined model of the condition of the wheeled vehicle, whereinthe input signals to said model include the first physical inputparameter (y1(t)), the second physical input parameter (y2(t)), a firstoffset scaling factor (c1(t)) for the first sensor signal, and a secondoffset scaling factor (c2(t)) for the second sensor signal, and whereinthe model output signals include a first offset error signal (b1(t)) anda second offset error signal (b2(t)), and the physical parameter value(X); (d) means for estimating the values of said first offset error(b1(t)) and the second offset error (b2(t)) by means of said adaptivefilter, wherein at least one offset error relates to the wheel radius;and (e) means for calculating the physical parameter value (X) using theadaptive filter from the input sensor signals y1(t) and y2(t) such thatoffset errors in the calculation are compensated for by means of thefirst and second offset error parameters (b1(t)) and (b2(t)) and theoffset scaling factors c1(t) and c2(t).
 46. The apparatus of claim 45,further comprising a processing unit (110,112,114,116,117) devised forcarrying out the functions related to said means.
 47. A computer programdirectly loadable into the internal memory of a digital computer,comprising program code for calculating a physical parameter value (X)of a wheeled vehicle indirectly using measurable input signals, theprogram code comprises sets of instructions for: (a) receiving a firstinput sensor signal (y1(t)) that is dependent on a first physical inputparameter affecting a condition of the wheeled vehicle; (b) receiving asecond input sensor signal (y2(t)) that is dependent on a secondphysical input parameter affecting a condition of the wheeled vehicle,wherein the second physical input parameter can be any one of the sameas physical parameter value (X), the same as the first physical inputparameter, and different from the first physical input parameter; (c)recursively filtering the first and second physical input parameters bymeans of an adaptive filter based on a predetermined model of thecondition of the wheeled vehicle, wherein the input signals to saidmodel include the first physical input parameter (yl(t)), the secondphysical input parameter (y2(t)), a first offset scaling factor (c1(t))for the first sensor signal, and a second offset scaling factor (c2(t))for the second sensor signal, and wherein the model output signalsinclude a first offset error signal (b1(t)) and a second offset errorsignal (b2(t)), and the physical parameter value (X); (d) estimating thevalues of said first offset error (b1(t)) and the second offset error(b2(t)) by means of said adaptive filter, wherein at least one offseterror relates to the wheel radius; and (e) calculating the physicalparameter value (X) using the adaptive filter from the input sensorsignals y1(t) and y2(t) such that offset errors in the calculation arecompensated for by means of the first and second offset error parameters(b1(t)) and (b2(t)) and the offset scaling factors c1(t) and c2(t). 48.A method of calculating a physical parameter value (X) of a wheeledvehicle indirectly by recursively filtering at least two measurableinput sensor signals, comprising the steps of: processing a plurality ofinput sensor signals (y1(t),y2(t)) that are dependent on first andsecond physical input parameters respectively that affect a condition ofthe wheeled vehicle; recursively filtering the first and second physicalinput parameters by means of an adaptive filter based on a predeterminedmodel of the condition of the wheeled vehicle, wherein the input signalsto said model include the first physical input parameter (y1(t)), thesecond physical input parameter (y2(t)), a first offset scaling factor(c1(t)) for the first sensor signal, and a second offset scaling factor(c2(t)) for the second sensor signal, and wherein the model outputsignals include a first offset error signal (b1(t)) and a second offseterror signal (b2(t)), and the physical parameter value (X); estimatingthe values of said first offset error (b1(t)) and said second offseterror (b2(t)) by means of recursively filtering with an adaptive filter,wherein at least one offset error relates to the wheel radius;calculating one or more physical parameter value (X) signals using theadaptive filter; and using the first and second offset errors(b1(t),b2(t)) to adjust the physical parameter values (X) to a valuethat is more representative of its actual value.